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Simplifying 46y2 + -84y + 24 = 0 Reorder the terms: 24 + -84y + 46y2 = 0 Solving 24 + -84y + 46y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -42y + 23y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -42y + 23y2)' equal to zero and attempt to solve: Simplifying 12 + -42y + 23y2 = 0 Solving 12 + -42y + 23y2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. 0.5217391304 + -1.826086957y + y2 = 0 Move the constant term to the right: Add '-0.5217391304' to each side of the equation. 0.5217391304 + -1.826086957y + -0.5217391304 + y2 = 0 + -0.5217391304 Reorder the terms: 0.5217391304 + -0.5217391304 + -1.826086957y + y2 = 0 + -0.5217391304 Combine like terms: 0.5217391304 + -0.5217391304 = 0.0000000000 0.0000000000 + -1.826086957y + y2 = 0 + -0.5217391304 -1.826086957y + y2 = 0 + -0.5217391304 Combine like terms: 0 + -0.5217391304 = -0.5217391304 -1.826086957y + y2 = -0.5217391304 The y term is -1.826086957y. Take half its coefficient (-0.9130434785). Square it (0.8336483936) and add it to both sides. Add '0.8336483936' to each side of the equation. -1.826086957y + 0.8336483936 + y2 = -0.5217391304 + 0.8336483936 Reorder the terms: 0.8336483936 + -1.826086957y + y2 = -0.5217391304 + 0.8336483936 Combine like terms: -0.5217391304 + 0.8336483936 = 0.3119092632 0.8336483936 + -1.826086957y + y2 = 0.3119092632 Factor a perfect square on the left side: (y + -0.9130434785)(y + -0.9130434785) = 0.3119092632 Calculate the square root of the right side: 0.558488373 Break this problem into two subproblems by setting (y + -0.9130434785) equal to 0.558488373 and -0.558488373.Subproblem 1
y + -0.9130434785 = 0.558488373 Simplifying y + -0.9130434785 = 0.558488373 Reorder the terms: -0.9130434785 + y = 0.558488373 Solving -0.9130434785 + y = 0.558488373 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9130434785' to each side of the equation. -0.9130434785 + 0.9130434785 + y = 0.558488373 + 0.9130434785 Combine like terms: -0.9130434785 + 0.9130434785 = 0.0000000000 0.0000000000 + y = 0.558488373 + 0.9130434785 y = 0.558488373 + 0.9130434785 Combine like terms: 0.558488373 + 0.9130434785 = 1.4715318515 y = 1.4715318515 Simplifying y = 1.4715318515Subproblem 2
y + -0.9130434785 = -0.558488373 Simplifying y + -0.9130434785 = -0.558488373 Reorder the terms: -0.9130434785 + y = -0.558488373 Solving -0.9130434785 + y = -0.558488373 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9130434785' to each side of the equation. -0.9130434785 + 0.9130434785 + y = -0.558488373 + 0.9130434785 Combine like terms: -0.9130434785 + 0.9130434785 = 0.0000000000 0.0000000000 + y = -0.558488373 + 0.9130434785 y = -0.558488373 + 0.9130434785 Combine like terms: -0.558488373 + 0.9130434785 = 0.3545551055 y = 0.3545551055 Simplifying y = 0.3545551055Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.4715318515, 0.3545551055}Solution
y = {1.4715318515, 0.3545551055}
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